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Deep neural network (DNN) and shallow NN (SNN) models are compared on various non-stationary time series prediction problems. The models include feedforward NNs (FNNs), Elman NNs (ENNs), Jordan NNs (JNNs), multi-recurrent NNs (MRNNs), time delay NNs (TDNNs), long short-term memory (LSTM) networks, gated recurrent unit (GRU) networks, recurrent convolutional NNs (RCNNs), and temporal convolutional NNs (TCNNs). Particle swarm optimization (PSO), adaptive moment estimation (Adam), resilient propagation (RPROP), and quantum PSO (QPSO) were used as training algorithms. The models are evaluated under different change severities and change frequencies. Results indicate that DNNs outperform SNNs. Further, results show that QPSO-trained FNNs outperform shallow recurrent NNs (SRNNs) trained using PSO, RPROP or QPSO. Additionally, the findings of the paper showed that DNNs trained using QPSO perform as well or better than DNNs trained using Adam.

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Forecasting Non-stationary Time Series: A Comparison of Deep and Shallow Neural Network Architectures

  • 会议论文

  • 发表日期：

    2026年

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  • Takudzwa Masunungure,
  • Andries Engelbrecht

摘要

Deep neural network (DNN) and shallow NN (SNN) models are compared on various non-stationary time series prediction problems. The models include feedforward NNs (FNNs), Elman NNs (ENNs), Jordan NNs (JNNs), multi-recurrent NNs (MRNNs), time delay NNs (TDNNs), long short-term memory (LSTM) networks, gated recurrent unit (GRU) networks, recurrent convolutional NNs (RCNNs), and temporal convolutional NNs (TCNNs). Particle swarm optimization (PSO), adaptive moment estimation (Adam), resilient propagation (RPROP), and quantum PSO (QPSO) were used as training algorithms. The models are evaluated under different change severities and change frequencies. Results indicate that DNNs outperform SNNs. Further, results show that QPSO-trained FNNs outperform shallow recurrent NNs (SRNNs) trained using PSO, RPROP or QPSO. Additionally, the findings of the paper showed that DNNs trained using QPSO perform as well or better than DNNs trained using Adam.